Name: Cherie Hua
Andrew ID: cxhua
This lab is to be begun in class, but may be finished outside of class at any time prior to Wednesday, September 16th at 6:00 PM. You must commit both the edited Rmd file and the “knitted” html file for this lab to your GitHub repo. (You can verbally discuss aspects of the labs with your classmates, but please do not share code, etc.)
We’ll begin by importing some data from the 36-290 GitHub site:
library(tidyverse)
## ── Attaching packages ───────────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.2 ✓ purrr 0.3.4
## ✓ tibble 3.0.3 ✓ dplyr 1.0.2
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0
## ── Conflicts ──────────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
rm(list=ls())
file.path = "https://raw.githubusercontent.com/pefreeman/36-290/master/EXAMPLE_DATASETS/DRACO/draco_photometry.Rdata"
load(url(file.path))
df = data.frame(ra,dec,velocity.los,log.g,temperature,mag.g,mag.i)
rm(file.path,ra,dec,velocity.los,log.g,temperature,mag.u,mag.g,mag.r,mag.i,mag.z,metallicity,signal.noise)
objects()
## [1] "df"
If everything loaded correctly, you should see one variable in your global environment: df. df is a data frame with 2778 rows and 7 columns. See this README file for a full description of the data and its variables. Note that I have removed signal.noise, metallicity, and three of the magnitudes from the data frame, to reduce the dimensionality and thus make analyses easier. To be clear: the data do not explicitly include a response variable. It’s just a multidimensional set of data.
This lab will be different from most if not all of the others, in that I want you to bring the tools that you’ve learned to bear by performing an exploratory analysis on the Draco dataset.
There are no “right answers” in this lab. It is more that some answers may be better (or more complete or tell a fuller story) than others.
Some things that you want to keep in mind:
temperature, say, it is sufficient to show one plot and mention how the other variable is not shown because the behavior is similar. Or something like that.ggplot, see this set of notes on correlation plots, pairs plots, etc..Variable_Transformations.pdf.plot(df)
if ( require(GGally) == FALSE ) {
install.packages("GGally",repos="https://cloud.r-project.org")
library(GGally)
}
## Loading required package: GGally
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
# Updated in 2020. Setting the color not working properly: TBD
df %>% select(.,ra,dec,velocity.los,log.g,temperature,mag.g,mag.i) %>% ggpairs(.,progress=FALSE,lower=list(combo=wrap("facethist", binwidth=0.8)))
ggplot(data=df, mapping = aes(x=ra, y=dec)) + geom_point(color = "olivedrab", size=0.5) + labs(x = "right ascension (degrees)", y = "declination (degrees)")
ggplot(data=df, mapping = aes(x=dec, y=log.g)) + geom_point(color = "olivedrab", size=0.5) + labs(x = "declination (degrees)", y = "log(surface gravity) (cgs)")
#dec - mag i is similar
#dec - mag g is similar
#dec - temperature is similar
ggplot(data=df, mapping = aes(x=velocity.los, y=temperature)) + geom_point(color = "olivedrab", size=0.5) + labs(x = "velocity (km/s)", y = "temperature (K)")
#velocity.los - ra is similar
#velocty.los - dec is similar
ggplot(data=df, mapping = aes(x=log.g, y=temperature)) + geom_point(color = "olivedrab", size=0.5) + labs(x = "log(surface gravity) (cgs)", y = "temperature")
#log.g - ra is similar
ggplot(data=df, mapping = aes(x=mag.g, y=mag.i)) + geom_point(color = "olivedrab", size=0.5) + labs(x = "magnitude - g", y = "magnitude - i")
ggplot(data=df, mapping = aes(x=ra, y=mag.i)) + geom_point(color = "olivedrab", size=0.5) + labs(x = "right ascension (degrees)", y = "magnitude - i")
#ra - magnitude g is similar]
ggplot(data=df, mapping = aes(x=ra, y=temperature)) + geom_point(color = "olivedrab", size=0.5) + labs(x = "right ascension (degrees)", y = "temperature")
#other variables involving temperature are similar
#ra,dec,velocity.los,log.g,temperature,mag.g,mag.i
ggplot(data=df,mapping=aes(x=ra)) + geom_histogram(fill = 'olivedrab1', bins = 60)
ggplot(data=df,mapping=aes(x=dec)) + geom_histogram(fill = 'olivedrab1', bins = 60)
ggplot(data=df,mapping=aes(x=velocity.los)) + geom_histogram(fill = 'olivedrab1', bins = 60)
ggplot(data=df,mapping=aes(x=log.g)) + geom_histogram(fill = 'olivedrab1', bins = 60)
ggplot(data=df,mapping=aes(x=temperature)) + geom_histogram(fill = 'olivedrab1', bins = 60)
ggplot(data=df,mapping=aes(x=mag.g)) + geom_histogram(fill = 'olivedrab1', bins = 60)
ggplot(data=df,mapping=aes(x=mag.i)) + geom_histogram(fill = 'olivedrab1', bins = 60)
ra - The data is skewed to the right with apparent outliers. dec - The data is skewed to the left with apparent outliers. velocity - The data seems to be bimodal with spikes to the left and right. It’s also very concentrated around the middle-left region. log.g - The data is also bimodel with spikes to the left and right, but covers a wder range. temperature - The data is skewed to the right. mag.g - The data is slightly skewed to the left with what appears to be two peaks. mag.i - Similar to mag.g except with more unclear peaks.
km.out = kmeans(df, 1)
km.out$cluster
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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## [1962] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1999] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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## [2110] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
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## [2702] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2739] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [2776] 1 1 1
plot(df, col=(km.out$cluster +1))
hc.complete=hclust(dist(df), method = 'complete')
plot(hc.complete ,main="Complete Linkage ")
hc.average = hclust(dist(df), method ="average")
plot(hc.average , main="Average Linkage")
hc.single = hclust(dist(df), method ="single")
plot(hc.single , main="Single Linkage ")